This combination of scattering lengths
would isolate the CIB contribution if \(N\!N\)  scattering were perturbative and Coulomb interactions absent, but in practice depends on all couplings in a complicated manner.
To obtain the numerical result we have used the empirical values \(a_{pp}^C=-7.817(4)\,\text{fm}\)  [1]}, [2]}, \(a_{np}=-23.74(2)\,\text{fm}\)  [3]}, [4]}, \(a_{nn}=-18.9(4)\,\text{fm}\)  [5]}. From Eq. (REF ) we find \(a_\text{CIB}=15.9^{+4.5}_{-4.0}\,\text{fm}\) , in good agreement with Eq. (REF ), given that additional uncertainties from higher chiral orders could be attached. The comparison to the phenomenology of CIB in \(N\!N\)  scattering thus validates our approach at the level of (30–50)% and shows that our uncertainty estimates are realistic.
